Robust Design Optimization of Tuned Mass Dampers in Structural Dynamics Using Efficient Reduced Order Models

In the following paper an optimization approach for the optimal design of tuned mass dampers in structural dynamics is presented. The approach considers uncertain system parameters and the tuned mass damper performance is measured by means of the total and relative displacements of the structure. In a first step, a single-degree-of-freedom system is investigated using an analytical formulation of the amplification function. The uncertainty propagation is implemented by an efficient linearization approach where each value of the amplification function is considered separately. The optimization goal functions are the minimization of the damper mass and the minimization of the maximum displacements by considering mean and standard deviation of the random system responses. The presented approach is extended for multi-degree-of-freedom systems by an efficient modal decomposition approach, which will be proven to be sufficiently accurate. By means of several examples, the overall robust design optimization procedure is discussed and different assumptions for the optimization goals and different optimization methods are investigated.